Sum of 5 Puzzle - Solution
The Puzzle:
A 5-digit number has the sum of all five digits equal to 5.
The first digit is equal to the number of zeros, the second digit is equal to the number of ones, and so on.
What is the number?
(Example that does NOT work: 30200 says "3 zeros, 2 twos", but there is only 1 two, so try again!)
Our Solution:
No digit should be 4, because that would mean 4 0s (total of 4), or 4 1s (total of 8), or higher, no total of 5 possible.
So the last digit must be 0 (there are zero 4's).
Also no digit should be 3, because that way 3 + 3x + y isn't 5, except if x = 0 and y = 2. However there aren't any digits that are twice in the sequence 3, x, x, x , 2.
So the final two digits are 0.
Now, 5 = 2 + 2 + 1 + 0 + 0. Now we notice that there are two zeros and two twos. So the first and third digits are 2, with the second being 1.
Answer: 21200.